Tuesday, July 10, 2012

Futures returns consist of two components: the returns of the spot price and the "roll returns". This is kind of obvious if you think about it: suppose the spot price remains constant in time (and therefore has zero return). Futures with different maturities will still have different prices at any point in time, and yet they must all converge to the same spot price at expirations, which means they must have non-zero returns during their lifetimes. This roll return is in action every day, not just during the rollover to the next nearest contract. For some futures, the magnitude of this roll return can be very large: it averages about -50% annualized for VX, the volatility futures. Wouldn't it be nice if we can somehow extract this return?

In theory, extracting this return should be easy: if a future is in backwardation (positive roll return), just buy the future and short the underlying asset, and vice versa if it is in contango. Unfortunately, shorting, or even buying, an underlying asset is not easy. Except for precious metals, most commodity ETFs that hold "commodities" actually hold only their futures (e.g. USO, UNG, ...), so they are of no help at all in this arbitrage strategy. Meanwhile, it is also a bit inconvenient for us to go out and buy a few oil tankers ourselves.

But in arbitrage trading, we often do not need an exact arbitrage relationship: a statistical likely relationship is good enough. So instead of using a commodity ETF as a hedge against the future, we can use a commodity-producer ETF. For example, instead of using USO as a hedge, we can use XLE, the energy sector ETF that holds energy producing companies. These ETFs should have a higher degree of correlation with the spot price than do the futures, and therefore very suitable as hedges. In cases where the futures do not track commodities (as in the case of VX), however, we have to look harder to find the proper hedge.

Which brings me to this fresh-off-the-press paper by David Simon and Jim Campasano. (Hat tip: Simon T.) This paper suggests a trading strategy that tries to extract the very juicy roll returns of VX. The hedge they suggest is -- you guessed it! -- the ES future. In a nutshell: if VX is in contango (which is most of the time), just short both VX and ES, and vice versa if VX is in backwardation.

Why does ES work as a good hedge? Of course, its very negative correlation with VX is the major factor. But one should not overlook the fact that ES also has a very small roll return (about +1.5% annualized). In other words, if you want to find a future to act as a hedge, look for ones that have an insignificant roll return. (Of course, if we can find a future that has high correlation with your original future but which has a high roll return of the opposite sign, that would be ideal. But we are seldom that lucky.)

P.S. The reader Simon who referred me to this paper also drew my attention to an apparent contradiction between its conclusion and my earlier blog post: Shorting the VIX Calendar Spread. This paper says that it is profitable to short VX when it is in contango and hedge with short ES, while I said it may not be profitable to short the front contract of VX when it is in contango and hedge with long back contract of VX. Both statements are true: hedging with the back contract of VX brings very little benefit because both the front and back contracts are suffering from very similar roll returns, so there is little return left when you take opposite positions in them!

This may not be the most relevant post for this question, but I am wondering whether there is any framework to optimize a futures portfolio. Most of the futures money management technique I have seen involve backing out dollar allocation for each contract based on leverage and maximum loss, for example. I was hoping to use the mean-variance type optimization in order to model the correlation, but I am not entirely sure how to model the leverage and margin into the optimization. Are you aware of any technique for this?

Hi ezbentley,Money management techniques for futures is the same as for any other instruments under the Kelly formula framework. All you need to make sure is that when calculating returns, you are using P&L/Market_value, so that no margin or leverage are involved.Kelly formula will tell you how much leverage to use.Ernie

Thanks for your reply. Just to clarify, are you suggesting to compute return and covariance matrix based on the raw prices, as if they are stocks? Then you take the leverage suggested by Kelly to decide the actual allocation? In other words, the margin imposed by the exchange never comes into play as long as the Kelly leverage is smaller than the margin-implied leverage. Is my understanding correct?

"Mkt Scanner" is used to find "liquid" stocks in the same "industry". It just groups stocks in the same "industry". Then we use these symbols in the same "industry" to download historical data. Then do numerical tests to find pairs.

It seems we test stocks pairs in the same "industry", but the "industry" definition is a little different in the different levels and systems.

Let me first congrats & thank you for your wonderful posts & very informative & extremely useful book (i am currently reading) .sir my name is amit,from india, i am a nanotech R&D.professional,i also wanna do algo trading,sir whether is it applicable for india as well? please guide .your little guidance will change the life of many layman like me.

sir i can offer free on/offline assistance to any assignment according to my skills,if you needed any time.

You often write about correlated/cointegrated stocks and mean reversion strategies. I´ve always wondered if this can be turned around. E.g. suppose that stock A and B historically don´t correlate at all - whenever their correlation coefficient is > 0,5 or < -0,5 it will most likely turn around and revert to 0. Could this be a basis of a strategy? Or probably not possible to model such phenomenon with orders in A and B?

You often write about correlated/cointegrated stocks and mean reversion strategies. I´ve always wondered if this can be turned around. E.g. suppose that stock A and B historically don´t correlate at all - whenever their correlation coefficient is > 0,5 or < -0,5 it will most likely turn around and revert to 0. Could this be a basis of a strategy? Or probably not possible to model such phenomenon with orders in A and B?

Thanks for your wonderful book! I have a question: for your calendar spread strategy to profit from roll return, we need to calculate the half life using gamma. In my backtest program, I was getting negative halflife at beginning, or very extreme large number, like 2000.

Only to realize, the amount of gammas that I feed into the halflife calculation is too little (a year or 252 days only). I increased the gammas count to 1000 using a lot more training data, then only the halflife start to make sense.

Assuming the halflife will not be constant, I modified your matlab code to using an updating halflife for everyday, and the Sharpe ratio and APR increased slightly for the same period.

I would like to know, do half life calculation always require this much of data? Since my training program is having problem referring to this much of expired contract.

The length of data that halflife calculation needs depends on the halflife itself (the longer the halflife, the more data needed), as well as on the stability of the mean-reversion. Some spreads undergo a period ("regime") of momentum or random walk that leads to negative or infinite halflife during such periods. So it becomes necessary to use a large amount of data to find its long-term behavior.

Hi VHanded,We can't really tell whether the period of momentum or random walk will be temporary or permanent unless you have some fundamental understanding of the pair. In any case, one should gradually decrease leverage in this situation.

It isn't really necessary to update half life every day. Probably monthly update is enough.